A-LevelMathematicsComplex numbers9709/31 · May/June 2024 · Q44 Marks
The complex number u is given by u = -1-i√3.
- (a)Express u in the form r (cosθ+isinθ), where r > 0 and -π < θ≤ π. Give the exact values of r and θ.[2]
- (b)The complex number v is given by v = 5(cos π/6 + i sin π/6). Express the complex number u/v in the form r eiθ where r > 0 and -π < θ≤ π.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] State or imply r = 2
- [B1] State or imply θ = -2π/3
- [B1FT] State or imply r = 5/2
- [B1FT] State or imply θ = π/6
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